Apart from that the guide probably could do with a note that export MB_env_key=env_value is equivalent to set in CMD.EXE and $env.MB_env_key = 'env_value' in Powershell for that matter I think it’s short sweet and to the point.
You don’t mention what you have tried - and what error/problem you get -
also what MySQL version are you using - note version 8 got released fairly recently and has issues - that is getting narrowed and nailed as we speak:
edit I just got the impulse that adding the environment variables to be part of the java command line arguments with -D definitions would make it agnostic to the OS, like so:
java -DMB_DB_TYPE=postgres ......<more> ... .. -jar .\metabase.jar ... <more> ...
If that is the stumbling block?